%I A008314
%S A008314 1,1,1,1,1,3,1,4,3,1,5,10,1,6,15,10,1,7,21,35,1,8,28,56,35,1,9,36,
%T A008314 84,126,1,10,45,120,210,126,1,11,55,165,330,462,1,12,66,220,
%U A008314 495,792,462,1,13,78,286,715,1287,1716,1,14,91,364,1001,2002,3003,1716,
               1,15,105,455,1365,3003,5005
%N A008314 Triangle of expansions of one half of powers of 2*x in terms of Chebyshev 
               polynomials T_n (x).
%C A008314 The entry a(0,0) should actually be 1/2.
%C A008314 The row lengths of this array are [1,1,2,2,3,3,...]= A004526.
%D A008314 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 795.
%D A008314 T. J. Rivlin, Chebyshev polynomials: from approximation theory to algebra 
               and number theory, 2. ed., Wiley, New York, 1990. p. 54-5, Ex.1.5.31.
%H A008314 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A008314 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%e A008314 [1/2], [1], [1,2/2=1], [1,3], [1,4,6/2=3], [1,5,10], [1,6,15,20/2=10],
               ...
%Y A008314 Cf. A008311.
%Y A008314 Bisection triangles: A122366 (odd numbered rows), A127673 (even numbered 
               rows).
%Y A008314 Sequence in context: A101038 A064883 A090844 this_sequence A104568 A030758 
               A104764
%Y A008314 Adjacent sequences: A008311 A008312 A008313 this_sequence A008315 A008316 
               A008317
%K A008314 nonn,tabf
%O A008314 0,6
%A A008314 N. J. A. Sloane (njas(AT)research.att.com).